# Conditional Sig-Wasserstein GANs for Time Series Generation

arXiv: https://arxiv.org/abs/2006.05421 · HTML: https://mlsanity.com/paper/2006.05421/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 23 of 23)

- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [The Volterra signature](https://mlsanity.com/paper/2603.04525/) (2026)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Synthetic Data for Portfolios: A Throw of the Dice Will Never Abolish Chance](https://mlsanity.com/paper/2501.03993/) (2025)
- [WaveStitch: Flexible and Fast Conditional Time Series Generation with Diffusion Models](https://mlsanity.com/paper/2503.06231/) (2025)
- [High Rank Path Development: an approach of learning the filtration of stochastic processes](https://mlsanity.com/paper/2405.14913/) (2024)
- [MCGAN: Enhancing GAN Training with Regression-Based Generator Loss](https://mlsanity.com/paper/2405.17191/) (2024)
- [Time Series Similarity Score Functions to Monitor and Interact with the Training and Denoising Process of a Time Series Diffusion Model applied to a Human Activity Recognition Dataset based on IMUs](https://mlsanity.com/paper/2505.14739/) (2025)
- [Semi-Supervised Bayesian GANs with Log-Signatures for Uncertainty-Aware Credit Card Fraud Detection](https://mlsanity.com/paper/2509.00931/) (2025)
- [Expected Signature Kernels for Rough Paths](https://mlsanity.com/paper/2509.07893/) (2025)
- [Diffolio: A Diffusion Model for Multivariate Probabilistic Financial Time-Series Forecasting and Portfolio Construction](https://mlsanity.com/paper/2511.07014/) (2025)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [Tensor-to-Tensor Models with Fast Iterated Sum Features](https://mlsanity.com/paper/2506.06041/) (2025)
- [Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization](https://mlsanity.com/paper/2509.22088/) (2025)
- [Effective Series Decomposition and Components Learning for Time Series Generation](https://mlsanity.com/paper/2511.00747/) (2025)
- [Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios](https://mlsanity.com/paper/2603.08553/) (2026)
- [Sampler-Robust Optimization under Generative Models](https://mlsanity.com/paper/2604.27447/) (2026)
- [Probabilistic Signature Inversion: Learning Conditional Distributions from Truncated Signatures](https://mlsanity.com/paper/2606.15332/) (2026)
- [From Jumps to Signatures: a Generative Method for Temporal Point Processes](https://mlsanity.com/paper/2607.06652/) (2026)
- [CodeTS: Verifiable Text-to-Time Series Generation via Executable Code](https://mlsanity.com/paper/2609.15393/) (2026)
- [Wavelet Flow Matching for Time Series](https://mlsanity.com/paper/2609.39374/) (2026)

## Abstract (arXiv)

Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high dimensional probability measures. However, these methods struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, long time-series data streams hugely increase the dimension of the target space, which may render generative modelling infeasible. To overcome these challenges, motivated by the autoregressive models in econometric, we are interested in the conditional distribution of future time series given the past information. We propose the generic conditional Sig-WGAN framework by integrating Wasserstein-GANs (WGANs) with mathematically principled and efficient path feature extraction called the signature of a path. The signature of a path is a graded sequence of statistics that provides a universal description for a stream of data, and its expected value characterises the law of the time-series model. In particular, we develop the conditional Sig-W1 metric, that captures the conditional joint law of time series models, and use it as a discriminator. The signature feature space enables the explicit representation of the proposed discriminators which alleviates the need for expensive training. We validate our method on both synthetic and empirical dataset and observe that our method consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.